Iron plates are required to have a certain thickness but each plate produced will differ slightly from each other due to properties of the material and uncertainties in the behaviour of the machines that make them. Let X be the plate thickness in mm of plates produced by a given machine. Using the machine's default setting, X follows a normal distribution with mean= 10mm and standard deviation 0.02mm (d) Find c > 0 to ensure that 5% of plates are expected to deviate in thickness by more than c mm from 10.00mm? (e) Given the c found in part (d), what percentage of plates are expected to deviate by more than c mm from 10.00mm if a slight adjustment in the machine shifts the expected value of X to 10.01mm
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Iron plates are required to have a certain thickness but each plate produced will differ slightly
from each other due to properties of the material and uncertainties in the behaviour of the machines
that make them. Let X be the plate thickness in mm of plates produced by a given machine. Using
the machine's default setting, X follows a
deviation 0.02mm
(d) Find c > 0 to ensure that 5% of plates are expected to deviate in thickness by more than c
mm from 10.00mm?
(e) Given the c found in part (d), what percentage of plates are expected to deviate by more than
c mm from 10.00mm if a slight adjustment in the machine shifts the
10.01mm
Step by step
Solved in 2 steps
